Question

Which are solutions of x2=-11+4?

Answer 1

ANSWER

$x = - \sqrt{ 7}i \: \: or \: \: x = + \sqrt{ 7}i$

EXPLANATION

The given expression is

${x}^{2} = - 11 + 4$

Simplify the left hand side to get:

${x}^{2} = - 7$

Take square root

$x = \pm \sqrt{ - 7}$

$x = \pm \sqrt{ 7} \times \sqrt{ - 1}$

Note that:

${i}^{2} = - 1 \implies \sqrt{ - 1} = i$

$x = \pm \sqrt{ 7}i$

Split the plus or minus sign

$x = - \sqrt{ 7}i \: \: or \: \: x = + \sqrt{ 7}i$

Answer 2

For this case we have a quadratic equation of the form:

$ax ^ 2 + bx + c = 0\\x ^ 2 + 11x-4 = 0$

Where:

$a = 1\\b = 11\\c = -4$

We find the roots:

$x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}\\x = \frac {-11 \pm \sqrt {11 ^ 2-4 (1) (- 4)}} {2 (1)}\\x = \frac {-11 \pm \sqrt {121 + 16}} {2}\\x = \frac {-11 \pm \sqrt {137}} {2}$

The roots are:

$x_ {1} = \frac {-11+ \sqrt {137}} {2}\\x_ {2} = \frac {-11- \sqrt {137}} {2}$

Answer:

$x_ {1} = \frac {-11+ \sqrt {137}} {2}\\x_ {2} = \frac {-11- \sqrt {137}} {2}$